LMFDB - Embedded newform 276.2.k.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	276.53
Dual form			276.2.k.a.125.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.751560 - 1.56050i) q^{3} +(1.12484 + 2.46306i) q^{5} +(1.26778 + 4.31765i) q^{7} +(-1.87032 + 2.34562i) q^{9} +O(q^{10})$	\(q+(-0.751560 - 1.56050i) q^{3} +(1.12484 + 2.46306i) q^{5} +(1.26778 + 4.31765i) q^{7} +(-1.87032 + 2.34562i) q^{9} +(-1.99770 - 2.30547i) q^{11} +(1.53595 + 0.450995i) q^{13} +(2.99822 - 3.60645i) q^{15} +(-0.816991 + 5.68230i) q^{17} +(5.10053 - 0.733345i) q^{19} +(5.78488 - 5.22334i) q^{21} +(3.34422 - 3.43747i) q^{23} +(-1.52710 + 1.76237i) q^{25} +(5.06599 + 1.15575i) q^{27} +(3.00513 + 0.432072i) q^{29} +(-6.72258 - 4.32034i) q^{31} +(-2.09629 + 4.85010i) q^{33} +(-9.20859 + 7.97929i) q^{35} +(0.490703 + 0.224097i) q^{37} +(-0.450579 - 2.73579i) q^{39} +(-3.17567 + 1.45028i) q^{41} +(-6.07336 - 9.45033i) q^{43} +(-7.88121 - 1.96825i) q^{45} -1.26989i q^{47} +(-11.1461 + 7.16314i) q^{49} +(9.48124 - 2.99567i) q^{51} +(1.39002 - 0.408147i) q^{53} +(3.43141 - 7.51374i) q^{55} +(-4.97774 - 7.40822i) q^{57} +(-3.86643 + 13.1679i) q^{59} +(3.06971 - 4.77657i) q^{61} +(-12.4987 - 5.10165i) q^{63} +(0.616871 + 4.29043i) q^{65} +(9.25358 + 8.01827i) q^{67} +(-7.87755 - 2.63519i) q^{69} +(4.56681 + 3.95716i) q^{71} +(-0.640452 - 4.45444i) q^{73} +(3.89788 + 1.05851i) q^{75} +(7.42156 - 11.5482i) q^{77} +(0.922489 - 3.14171i) q^{79} +(-2.00384 - 8.77409i) q^{81} +(5.09635 - 11.1595i) q^{83} +(-14.9148 + 4.37939i) q^{85} +(-1.58429 - 5.01423i) q^{87} +(1.32007 - 0.848360i) q^{89} +7.20344i q^{91} +(-1.68947 + 13.7376i) q^{93} +(7.54357 + 11.7380i) q^{95} +(7.14563 - 3.26330i) q^{97} +(9.14407 - 0.373885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.751560	−	1.56050i	−0.433913	−	0.900955i
$3$	−0.751560	−	1.56050i	−0.433913	−	0.900955i
$4$		0			0
$5$	1.12484	+	2.46306i	0.503045	+	1.10151i	0.975468	+	0.220143i	$0.0706523\pi$
$5$	1.12484	+	2.46306i	0.503045	+	1.10151i	−0.472423	+	0.881372i	$0.656620\pi$
$6$		0			0
$7$	1.26778	+	4.31765i	0.479174	+	1.63192i	0.744402	+	0.667732i	$0.232735\pi$
$7$	1.26778	+	4.31765i	0.479174	+	1.63192i	−0.265227	+	0.964186i	$0.585447\pi$
$8$		0			0
$9$	−1.87032	+	2.34562i	−0.623438	+	0.781872i
$10$		0			0
$11$	−1.99770	−	2.30547i	−0.602329	−	0.695124i	0.369923	−	0.929062i	$-0.379384\pi$
$11$	−1.99770	−	2.30547i	−0.602329	−	0.695124i	−0.972251	+	0.233938i	$0.924839\pi$
$12$		0			0
$13$	1.53595	+	0.450995i	0.425995	+	0.125083i	0.487701	−	0.873011i	$-0.337836\pi$
$13$	1.53595	+	0.450995i	0.425995	+	0.125083i	−0.0617056	+	0.998094i	$0.519654\pi$
$14$		0			0
$15$	2.99822	−	3.60645i	0.774137	−	0.931183i
$16$		0			0
$17$	−0.816991	+	5.68230i	−0.198150	+	1.37816i	0.611499	+	0.791245i	$0.290567\pi$
$17$	−0.816991	+	5.68230i	−0.198150	+	1.37816i	−0.809649	+	0.586915i	$0.800342\pi$
$18$		0			0
$19$	5.10053	−	0.733345i	1.17014	−	0.168241i	0.470278	−	0.882518i	$-0.344154\pi$
$19$	5.10053	−	0.733345i	1.17014	−	0.168241i	0.699863	+	0.714277i	$0.253244\pi$
$20$		0			0
$21$	5.78488	−	5.22334i	1.26236	−	1.13983i
$22$		0			0
$23$	3.34422	−	3.43747i	0.697318	−	0.716762i
$23$	3.34422	−	3.43747i	0.697318	−	0.716762i
$24$		0			0
$25$	−1.52710	+	1.76237i	−0.305420	+	0.352473i
$26$		0			0
$27$	5.06599	+	1.15575i	0.974950	+	0.222425i
$28$		0			0
$29$	3.00513	+	0.432072i	0.558039	+	0.0802338i	0.415563	−	0.909564i	$-0.363585\pi$
$29$	3.00513	+	0.432072i	0.558039	+	0.0802338i	0.142476	+	0.989798i	$0.454494\pi$
$30$		0			0
$31$	−6.72258	−	4.32034i	−1.20741	−	0.775956i	−0.227188	−	0.973851i	$-0.572953\pi$
$31$	−6.72258	−	4.32034i	−1.20741	−	0.775956i	−0.980223	+	0.197894i	$0.936590\pi$
$32$		0			0
$33$	−2.09629	+	4.85010i	−0.364917	+	0.844294i
$34$		0			0
$35$	−9.20859	+	7.97929i	−1.55654	+	1.34875i
$36$		0			0
$37$	0.490703	+	0.224097i	0.0806711	+	0.0368413i	0.455342	−	0.890317i	$-0.349517\pi$
$37$	0.490703	+	0.224097i	0.0806711	+	0.0368413i	−0.374671	+	0.927158i	$0.622244\pi$
$38$		0			0
$39$	−0.450579	−	2.73579i	−0.0721504	−	0.438077i
$40$		0			0
$41$	−3.17567	+	1.45028i	−0.495956	+	0.226496i	−0.647659	−	0.761931i	$-0.724252\pi$
$41$	−3.17567	+	1.45028i	−0.495956	+	0.226496i	0.151703	+	0.988426i	$0.451524\pi$
$42$		0			0
$43$	−6.07336	−	9.45033i	−0.926179	−	1.44116i	−0.897221	−	0.441581i	$-0.854418\pi$
$43$	−6.07336	−	9.45033i	−0.926179	−	1.44116i	−0.0289574	−	0.999581i	$-0.509219\pi$
$44$		0			0
$45$	−7.88121	−	1.96825i	−1.17486	−	0.293410i
$46$		0			0
$47$		−	1.26989i		−	0.185233i	−0.995702	−	0.0926164i	$-0.970477\pi$
$47$		−	1.26989i		−	0.185233i	0.995702	−	0.0926164i	$-0.0295230\pi$
$48$		0			0
$49$	−11.1461	+	7.16314i	−1.59230	+	1.02331i
$50$		0			0
$51$	9.48124	−	2.99567i	1.32764	−	0.419478i
$52$		0			0
$53$	1.39002	−	0.408147i	0.190934	−	0.0560633i	−0.184868	−	0.982763i	$-0.559186\pi$
$53$	1.39002	−	0.408147i	0.190934	−	0.0560633i	0.375802	+	0.926700i	$0.377367\pi$
$54$		0			0
$55$	3.43141	−	7.51374i	0.462691	−	1.01315i
$56$		0			0
$57$	−4.97774	−	7.40822i	−0.659317	−	0.981242i
$58$		0			0
$59$	−3.86643	+	13.1679i	−0.503366	+	1.71431i	0.179494	+	0.983759i	$0.442554\pi$
$59$	−3.86643	+	13.1679i	−0.503366	+	1.71431i	−0.682860	+	0.730549i	$0.739264\pi$
$60$		0			0
$61$	3.06971	−	4.77657i	0.393036	−	0.611577i	−0.587192	−	0.809448i	$-0.699766\pi$
$61$	3.06971	−	4.77657i	0.393036	−	0.611577i	0.980228	+	0.197871i	$0.0634028\pi$
$62$		0			0
$63$	−12.4987	−	5.10165i	−1.57469	−	0.642747i
$64$		0			0
$65$	0.616871	+	4.29043i	0.0765134	+	0.532162i
$66$		0			0
$67$	9.25358	+	8.01827i	1.13050	+	0.979588i	0.999930	−	0.0118504i	$-0.00377218\pi$
$67$	9.25358	+	8.01827i	1.13050	+	0.979588i	0.130575	+	0.991438i	$0.458318\pi$
$68$		0			0
$69$	−7.87755	−	2.63519i	−0.948346	−	0.317239i
$70$		0			0
$71$	4.56681	+	3.95716i	0.541980	+	0.469629i	0.882304	−	0.470680i	$-0.155991\pi$
$71$	4.56681	+	3.95716i	0.541980	+	0.469629i	−0.340324	+	0.940308i	$0.610537\pi$
$72$		0			0
$73$	−0.640452	−	4.45444i	−0.0749592	−	0.521353i	−0.992359	−	0.123386i	$-0.960625\pi$
$73$	−0.640452	−	4.45444i	−0.0749592	−	0.521353i	0.917400	−	0.397967i	$-0.130284\pi$
$74$		0			0
$75$	3.89788	+	1.05851i	0.450088	+	0.122227i
$76$		0			0
$77$	7.42156	−	11.5482i	0.845766	−	1.31604i
$78$		0			0
$79$	0.922489	−	3.14171i	0.103788	−	0.353470i	−0.891182	−	0.453647i	$-0.850123\pi$
$79$	0.922489	−	3.14171i	0.103788	−	0.353470i	0.994970	+	0.100177i	$0.0319409\pi$
$80$		0			0
$81$	−2.00384	−	8.77409i	−0.222649	−	0.974899i
$82$		0			0
$83$	5.09635	−	11.1595i	0.559397	−	1.22491i	−0.392856	−	0.919600i	$-0.628513\pi$
$83$	5.09635	−	11.1595i	0.559397	−	1.22491i	0.952253	−	0.305309i	$-0.0987599\pi$
$84$		0			0
$85$	−14.9148	+	4.37939i	−1.61774	+	0.475012i
$86$		0			0
$87$	−1.58429	−	5.01423i	−0.169853	−	0.537582i
$88$		0			0
$89$	1.32007	−	0.848360i	0.139927	−	0.0899259i	−0.468804	−	0.883302i	$-0.655315\pi$
$89$	1.32007	−	0.848360i	0.139927	−	0.0899259i	0.608732	+	0.793376i	$0.291679\pi$
$90$		0			0
$91$			7.20344i			0.755126i
$92$		0			0
$93$	−1.68947	+	13.7376i	−0.175190	+	1.42452i
$94$		0			0
$95$	7.54357	+	11.7380i	0.773954	+	1.20430i
$96$		0			0
$97$	7.14563	−	3.26330i	0.725528	−	0.331338i	−0.0181865	−	0.999835i	$-0.505789\pi$
$97$	7.14563	−	3.26330i	0.725528	−	0.331338i	0.743715	+	0.668497i	$0.233062\pi$
$98$		0			0
$99$	9.14407	−	0.373885i	0.919013	−	0.0375769i
$100$		0			0
$101$	−4.82923	−	2.20544i	−0.480526	−	0.219449i	0.160399	−	0.987052i	$-0.448722\pi$
$101$	−4.82923	−	2.20544i	−0.480526	−	0.219449i	−0.640925	+	0.767603i	$0.721449\pi$
$102$		0			0
$103$	2.16061	−	1.87218i	0.212891	−	0.184471i	−0.541887	−	0.840451i	$-0.682290\pi$
$103$	2.16061	−	1.87218i	0.212891	−	0.184471i	0.754778	+	0.655980i	$0.227745\pi$
$104$		0			0
$105$	19.3725	+	8.37308i	1.89056	+	0.817129i
$106$		0			0
$107$	−14.6202	−	9.39581i	−1.41338	−	0.908327i	−0.413387	−	0.910556i	$-0.635654\pi$
$107$	−14.6202	−	9.39581i	−1.41338	−	0.908327i	−0.999998	+	0.00222855i	$0.999291\pi$
$108$		0			0
$109$	0.151166	+	0.0217344i	0.0144791	+	0.00208178i	0.149551	−	0.988754i	$-0.452217\pi$
$109$	0.151166	+	0.0217344i	0.0144791	+	0.00208178i	−0.135071	+	0.990836i	$0.543126\pi$
$110$		0			0
$111$	−0.0190902	−	0.934164i	−0.00181196	−	0.0886669i
$112$		0			0
$113$	7.51191	−	8.66921i	0.706662	−	0.815531i	−0.282975	−	0.959127i	$-0.591321\pi$
$113$	7.51191	−	8.66921i	0.706662	−	0.815531i	0.989636	+	0.143596i	$0.0458667\pi$
$114$		0			0
$115$	12.2284	+	4.37040i	1.14031	+	0.407542i
$116$		0			0
$117$	−3.93056	+	2.75924i	−0.363381	+	0.255092i
$118$		0			0
$119$	−25.5699	+	3.67640i	−2.34399	+	0.337015i
$120$		0			0
$121$	0.241085	−	1.67678i	0.0219168	−	0.152435i
$122$		0			0
$123$	4.64986	+	3.86566i	0.419264	+	0.348554i
$124$		0			0
$125$	6.93180	+	2.03536i	0.619999	+	0.182048i
$126$		0			0
$127$	−4.94146	−	5.70275i	−0.438483	−	0.506037i	0.492895	−	0.870089i	$-0.335939\pi$
$127$	−4.94146	−	5.70275i	−0.438483	−	0.506037i	−0.931379	+	0.364052i	$0.881393\pi$
$128$		0			0
$129$	−10.1827	+	16.5800i	−0.896540	+	1.45978i
$130$		0			0
$131$	−1.62291	−	5.52712i	−0.141794	−	0.482907i	0.857718	−	0.514120i	$-0.171881\pi$
$131$	−1.62291	−	5.52712i	−0.141794	−	0.482907i	−0.999513	+	0.0312126i	$0.990063\pi$
$132$		0			0
$133$	9.63266	+	21.0926i	0.835257	+	1.82896i
$134$		0			0
$135$	2.85175	+	13.7779i	0.245439	+	1.18581i
$136$		0			0
$137$	−7.44527			−0.636092			−0.318046	−	0.948075i	$-0.603027\pi$
$137$	−7.44527			−0.636092			−0.318046	+	0.948075i	$0.603027\pi$
$138$		0			0
$139$	1.49086			0.126453			0.0632265	−	0.997999i	$-0.479861\pi$
$139$	1.49086			0.126453			0.0632265	+	0.997999i	$0.479861\pi$
$140$		0			0
$141$	−1.98167	+	0.954400i	−0.166886	+	0.0803750i
$142$		0			0
$143$	−2.02860	−	4.44202i	−0.169640	−	0.371461i
$144$		0			0
$145$	2.31608	+	7.88783i	0.192340	+	0.655049i
$146$		0			0
$147$	19.5550	+	12.0099i	1.61287	+	0.990560i
$148$		0			0
$149$	1.66932	+	1.92649i	0.136756	+	0.157824i	0.819996	−	0.572369i	$-0.193975\pi$
$149$	1.66932	+	1.92649i	0.136756	+	0.157824i	−0.683241	+	0.730193i	$0.739430\pi$
$150$		0			0
$151$	−10.4768	−	3.07625i	−0.852587	−	0.250342i	−0.173894	−	0.984764i	$-0.555635\pi$
$151$	−10.4768	−	3.07625i	−0.852587	−	0.250342i	−0.678693	+	0.734422i	$0.737453\pi$
$152$		0			0
$153$	−11.8005	−	12.5440i	−0.954011	−	1.01413i
$154$		0			0
$155$	3.07942	−	21.4178i	0.247345	−	1.72032i
$156$		0			0
$157$	20.3842	−	2.93081i	1.62684	−	0.233904i	0.732329	−	0.680951i	$-0.238433\pi$
$157$	20.3842	−	2.93081i	1.62684	−	0.233904i	0.894511	+	0.447046i	$0.147524\pi$
$158$		0			0
$159$	−1.68160	−	1.86238i	−0.133359	−	0.147696i
$160$		0			0
$161$	19.0815	+	10.0812i	1.50383	+	0.794512i
$162$		0			0
$163$	−7.99173	+	9.22295i	−0.625960	+	0.722397i	−0.976827	−	0.214028i	$-0.931341\pi$
$163$	−7.99173	+	9.22295i	−0.625960	+	0.722397i	0.350867	+	0.936425i	$0.385887\pi$
$164$		0			0
$165$	−14.3041	+	0.292313i	−1.11357	+	0.0227565i
$166$		0			0
$167$	14.5291	+	2.08897i	1.12430	+	0.161649i	0.679284	−	0.733876i	$-0.262290\pi$
$167$	14.5291	+	2.08897i	1.12430	+	0.161649i	0.445012	+	0.895525i	$0.353200\pi$
$168$		0			0
$169$	−8.78056	−	5.64292i	−0.675428	−	0.434071i
$170$		0			0
$171$	−7.81945	+	13.3355i	−0.597968	+	1.01979i
$172$		0			0
$173$	17.0917	−	14.8101i	1.29946	−	1.12599i	0.315246	−	0.949010i	$-0.397913\pi$
$173$	17.0917	−	14.8101i	1.29946	−	1.12599i	0.984215	−	0.176979i	$-0.0566323\pi$
$174$		0			0
$175$	−9.54531	−	4.35920i	−0.721557	−	0.329524i
$176$		0			0
$177$	23.4543	−	3.86287i	1.76293	−	0.290351i
$178$		0			0
$179$	11.2001	−	5.11491i	0.837135	−	0.382307i	0.0497450	−	0.998762i	$-0.484159\pi$
$179$	11.2001	−	5.11491i	0.837135	−	0.382307i	0.787390	+	0.616455i	$0.211432\pi$
$180$		0			0
$181$	3.83496	+	5.96732i	0.285051	+	0.443547i	0.954020	−	0.299742i	$-0.0969007\pi$
$181$	3.83496	+	5.96732i	0.285051	+	0.443547i	−0.668970	+	0.743290i	$0.733264\pi$
$182$		0			0
$183$	−9.76090	−	1.20041i	−0.721547	−	0.0887368i
$184$		0			0
$185$			1.46071i			0.107393i
$186$		0			0
$187$	14.7325	−	9.46797i	1.07734	−	0.692367i
$188$		0			0
$189$	1.43240	+	23.3384i	0.104192	+	1.69762i
$190$		0			0
$191$	−22.1408	+	6.50114i	−1.60206	+	0.470406i	−0.956117	−	0.292984i	$-0.905352\pi$
$191$	−22.1408	+	6.50114i	−1.60206	+	0.470406i	−0.645938	+	0.763390i	$0.723534\pi$
$192$		0			0
$193$	2.01653	−	4.41559i	0.145153	−	0.317841i	−0.823065	−	0.567947i	$-0.807738\pi$
$193$	2.01653	−	4.41559i	0.145153	−	0.317841i	0.968219	+	0.250105i	$0.0804653\pi$
$194$		0			0
$195$	6.23160	−	4.18714i	0.446254	−	0.299847i
$196$		0			0
$197$	2.01898	−	6.87601i	0.143846	−	0.489896i	−0.855777	−	0.517345i	$-0.826920\pi$
$197$	2.01898	−	6.87601i	0.143846	−	0.489896i	0.999623	+	0.0274494i	$0.00873852\pi$
$198$		0			0
$199$	−10.6229	+	16.5295i	−0.753037	+	1.17175i	0.227186	+	0.973851i	$0.427048\pi$
$199$	−10.6229	+	16.5295i	−0.753037	+	1.17175i	−0.980223	+	0.197897i	$0.936589\pi$
$200$		0			0
$201$	5.55789	−	20.4664i	0.392023	−	1.44359i
$202$		0			0
$203$	1.94429	+	13.5229i	0.136463	+	0.949119i
$204$		0			0
$205$	−7.14426	−	6.19053i	−0.498976	−	0.432366i
$206$		0			0
$207$	1.80825	+	14.2734i	0.125682	+	0.992071i
$208$		0			0
$209$	−11.8800	−	10.2941i	−0.821758	−	0.712057i
$210$		0			0
$211$	1.50772	+	10.4864i	0.103796	+	0.721916i	0.973557	+	0.228444i	$0.0733637\pi$
$211$	1.50772	+	10.4864i	0.103796	+	0.721916i	−0.869761	+	0.493473i	$0.835727\pi$
$212$		0			0
$213$	2.74292	−	10.1005i	0.187942	−	0.692078i
$214$		0			0
$215$	16.4452	−	25.5892i	1.12155	−	1.74517i
$216$		0			0
$217$	10.1310	−	34.5030i	0.687737	−	2.34222i
$218$		0			0
$219$	−6.46981	+	4.34720i	−0.437189	+	0.293757i
$220$		0			0
$221$	−3.81754	+	8.35925i	−0.256796	+	0.562304i
$222$		0			0
$223$	−7.42016	+	2.17876i	−0.496891	+	0.145900i	−0.520570	−	0.853819i	$-0.674280\pi$
$223$	−7.42016	+	2.17876i	−0.496891	+	0.145900i	0.0236786	+	0.999720i	$0.492462\pi$
$224$		0			0
$225$	−1.27768	−	6.87818i	−0.0851787	−	0.458545i
$226$		0			0
$227$	−12.5920	+	8.09239i	−0.835760	+	0.537110i	−0.887103	−	0.461571i	$-0.847286\pi$
$227$	−12.5920	+	8.09239i	−0.835760	+	0.537110i	0.0513433	+	0.998681i	$0.483650\pi$
$228$		0			0
$229$		−	16.0610i		−	1.06134i	−0.847578	−	0.530671i	$-0.821940\pi$
$229$		−	16.0610i		−	1.06134i	0.847578	−	0.530671i	$-0.178060\pi$
$230$		0			0
$231$	−23.5987	−	2.90220i	−1.55268	−	0.190950i
$232$		0			0
$233$	12.1424	+	18.8940i	0.795478	+	1.23779i	0.967544	+	0.252702i	$0.0813193\pi$
$233$	12.1424	+	18.8940i	0.795478	+	1.23779i	−0.172066	+	0.985085i	$0.555044\pi$
$234$		0			0
$235$	3.12782	−	1.42843i	0.204037	−	0.0931804i
$236$		0			0
$237$	−5.59594	+	0.921639i	−0.363495	+	0.0598669i
$238$		0			0
$239$	4.60144	+	2.10141i	0.297642	+	0.135929i	0.558639	−	0.829411i	$-0.311324\pi$
$239$	4.60144	+	2.10141i	0.297642	+	0.135929i	−0.260996	+	0.965340i	$0.584051\pi$
$240$		0			0
$241$	−18.0289	+	15.6221i	−1.16134	+	1.00631i	−0.161533	+	0.986867i	$0.551644\pi$
$241$	−18.0289	+	15.6221i	−1.16134	+	1.00631i	−0.999811	+	0.0194434i	$0.993811\pi$
$242$		0			0
$243$	−12.1860	+	9.72124i	−0.781729	+	0.623618i
$244$		0			0
$245$	−30.1808	−	19.3960i	−1.92818	−	1.23917i
$246$		0			0
$247$	8.16487	+	1.17393i	0.519518	+	0.0746955i
$248$		0			0
$249$	−21.2445	+	0.434145i	−1.34632	+	0.0275128i
$250$		0			0
$251$	14.3488	−	16.5594i	0.905689	−	1.04522i	−0.0930821	−	0.995658i	$-0.529672\pi$
$251$	14.3488	−	16.5594i	0.905689	−	1.04522i	0.998771	−	0.0495623i	$-0.0157826\pi$
$252$		0			0
$253$	−14.6057	−	0.842957i	−0.918253	−	0.0529962i
$254$		0			0
$255$	18.0434	+	19.9832i	1.12992	+	1.25140i
$256$		0			0
$257$	−13.5419	+	1.94703i	−0.844721	+	0.121453i	−0.551069	−	0.834460i	$-0.685780\pi$
$257$	−13.5419	+	1.94703i	−0.844721	+	0.121453i	−0.293652	+	0.955912i	$0.594871\pi$
$258$		0			0
$259$	−0.345469	+	2.40279i	−0.0214664	+	0.149302i
$260$		0			0
$261$	−6.63402	+	6.24077i	−0.410635	+	0.386294i
$262$		0			0
$263$	−21.8527	−	6.41652i	−1.34749	−	0.395660i	−0.473156	−	0.880978i	$-0.656885\pi$
$263$	−21.8527	−	6.41652i	−1.34749	−	0.395660i	−0.874337	+	0.485319i	$0.838704\pi$
$264$		0			0
$265$	2.56885	+	2.96461i	0.157803	+	0.182114i
$266$		0			0
$267$	−2.31598	−	1.42238i	−0.141736	−	0.0870483i
$268$		0			0
$269$	−1.25215	−	4.26444i	−0.0763451	−	0.260007i	0.912472	−	0.409138i	$-0.134171\pi$
$269$	−1.25215	−	4.26444i	−0.0763451	−	0.260007i	−0.988817	+	0.149131i	$0.952352\pi$
$270$		0			0
$271$	2.30679	+	5.05117i	0.140128	+	0.306837i	0.966665	−	0.256045i	$-0.0824197\pi$
$271$	2.30679	+	5.05117i	0.140128	+	0.306837i	−0.826537	+	0.562882i	$0.809692\pi$
$272$		0			0
$273$	11.2410	−	5.41382i	0.680334	−	0.327659i
$274$		0			0
$275$	7.11376			0.428976
$276$		0			0
$277$	7.56079			0.454284			0.227142	−	0.973862i	$-0.427062\pi$
$277$	7.56079			0.454284			0.227142	+	0.973862i	$0.427062\pi$
$278$		0			0
$279$	22.7072	−	7.68821i	1.35945	−	0.460281i
$280$		0			0
$281$	7.88342	+	17.2623i	0.470285	+	1.02978i	0.985021	+	0.172433i	$0.0551627\pi$
$281$	7.88342	+	17.2623i	0.470285	+	1.02978i	−0.514736	+	0.857349i	$0.672110\pi$
$282$		0			0
$283$	−1.77373	−	6.04078i	−0.105437	−	0.359087i	0.889826	−	0.456300i	$-0.150825\pi$
$283$	−1.77373	−	6.04078i	−0.105437	−	0.359087i	−0.995264	+	0.0972127i	$0.969007\pi$
$284$		0			0
$285$	12.6477	−	20.5936i	0.749187	−	1.21986i
$286$		0			0
$287$	−10.2878	−	11.8728i	−0.607272	−	0.700829i
$288$		0			0
$289$	−15.3097	−	4.49533i	−0.900569	−	0.264431i
$290$		0			0
$291$	−10.4627	−	8.69818i	−0.613337	−	0.509896i
$292$		0			0
$293$	−1.01869	+	7.08513i	−0.0595123	+	0.413917i	0.938187	+	0.346128i	$0.112504\pi$
$293$	−1.01869	+	7.08513i	−0.0595123	+	0.413917i	−0.997700	+	0.0677895i	$0.978405\pi$
$294$		0			0
$295$	−36.7824	+	5.28850i	−2.14155	+	0.307909i
$296$		0			0
$297$	−7.45576	−	13.9883i	−0.432627	−	0.811684i
$298$		0			0
$299$	6.68682	−	3.77155i	0.386709	−	0.218114i
$300$		0			0
$301$	33.1036	−	38.2035i	1.90806	−	2.20202i
$302$		0			0
$303$	0.187875	+	9.19353i	0.0107932	+	0.528154i
$304$		0			0
$305$	15.2179	+	2.18801i	0.871376	+	0.125285i
$306$		0			0
$307$	17.5497	+	11.2785i	1.00162	+	0.643700i	0.935210	−	0.354092i	$-0.115210\pi$
$307$	17.5497	+	11.2785i	1.00162	+	0.643700i	0.0664067	+	0.997793i	$0.478847\pi$
$308$		0			0
$309$	−4.54535	−	1.96457i	−0.258576	−	0.111761i
$310$		0			0
$311$	−3.71592	+	3.21986i	−0.210710	+	0.182582i	−0.753822	−	0.657079i	$-0.771792\pi$
$311$	−3.71592	+	3.21986i	−0.210710	+	0.182582i	0.543111	+	0.839661i	$0.317246\pi$
$312$		0			0
$313$	12.2662	+	5.60179i	0.693327	+	0.316632i	0.730728	−	0.682668i	$-0.239181\pi$
$313$	12.2662	+	5.60179i	0.693327	+	0.316632i	−0.0374011	+	0.999300i	$0.511908\pi$
$314$		0			0
$315$	−1.49339	−	36.5236i	−0.0841429	−	2.05787i
$316$		0			0
$317$	−8.97371	+	4.09815i	−0.504014	+	0.230175i	−0.651161	−	0.758939i	$-0.725718\pi$
$317$	−8.97371	+	4.09815i	−0.504014	+	0.230175i	0.147148	+	0.989114i	$0.452991\pi$
$318$		0			0
$319$	−5.00721	−	7.79138i	−0.280350	−	0.436233i
$320$		0			0
$321$	−3.67422	+	29.8763i	−0.205075	+	1.66753i
$322$		0			0
$323$			29.5819i			1.64598i
$324$		0			0
$325$	−3.14036	+	2.01819i	−0.174196	+	0.111949i
$326$		0			0
$327$	−0.0796938	−	0.252229i	−0.00440708	−	0.0139483i
$328$		0			0
$329$	5.48295	−	1.60994i	0.302285	−	0.0887588i
$330$		0			0
$331$	−1.53630	+	3.36403i	−0.0844426	+	0.184904i	−0.947143	−	0.320812i	$-0.896044\pi$
$331$	−1.53630	+	3.36403i	−0.0844426	+	0.184904i	0.862700	+	0.505716i	$0.168771\pi$
$332$		0			0
$333$	−1.44341	+	0.731870i	−0.0790986	+	0.0401062i
$334$		0			0
$335$	−9.34068	+	31.8114i	−0.510336	+	1.73804i
$336$		0			0
$337$	−10.8614	+	16.9007i	−0.591661	+	0.920642i	0.408309	+	0.912844i	$0.366119\pi$
$337$	−10.8614	+	16.9007i	−0.591661	+	0.920642i	−0.999970	+	0.00779817i	$0.997518\pi$
$338$		0			0
$339$	−19.1740	−	5.20691i	−1.04139	−	0.282800i
$340$		0			0
$341$	3.46929	+	24.1294i	0.187873	+	1.30668i
$342$		0			0
$343$	−21.2529	−	18.4158i	−1.14755	−	0.994358i
$344$		0			0
$345$	−2.37038	−	22.3671i	−0.127617	−	1.20420i
$346$		0			0
$347$	−6.98439	−	6.05201i	−0.374942	−	0.324889i	0.446922	−	0.894573i	$-0.352520\pi$
$347$	−6.98439	−	6.05201i	−0.374942	−	0.324889i	−0.821864	+	0.569684i	$0.807066\pi$
$348$		0			0
$349$	0.0491333	+	0.341730i	0.00263005	+	0.0182924i	0.991094	−	0.133163i	$-0.0425132\pi$
$349$	0.0491333	+	0.341730i	0.00263005	+	0.0182924i	−0.988464	+	0.151455i	$0.951604\pi$
$350$		0			0
$351$	7.25985	+	4.05991i	0.387502	+	0.216702i
$352$		0			0
$353$	16.6725	−	25.9429i	0.887385	−	1.38080i	−0.0369903	−	0.999316i	$-0.511777\pi$
$353$	16.6725	−	25.9429i	0.887385	−	1.38080i	0.924376	−	0.381483i	$-0.124587\pi$
$354$		0			0
$355$	−4.60979	+	15.6995i	−0.244662	+	0.833244i
$356$		0			0
$357$	24.9544	+	37.1388i	1.32073	+	1.96560i
$358$		0			0
$359$	4.34295	−	9.50974i	0.229212	−	0.501905i	−0.759724	−	0.650246i	$-0.774666\pi$
$359$	4.34295	−	9.50974i	0.229212	−	0.501905i	0.988936	+	0.148341i	$0.0473933\pi$
$360$		0			0
$361$	7.24722	−	2.12798i	0.381433	−	0.111999i
$362$		0			0
$363$	−2.79781	+	0.883990i	−0.146847	+	0.0463974i
$364$		0			0
$365$	10.2512	−	6.58802i	0.536570	−	0.344833i
$366$		0			0
$367$		−	14.9966i		−	0.782814i	−0.920218	−	0.391407i	$-0.871989\pi$
$367$		−	14.9966i		−	0.782814i	0.920218	−	0.391407i	$-0.128011\pi$
$368$		0			0
$369$	2.53770	−	10.1614i	0.132107	−	0.528980i
$370$		0			0
$371$	3.52447	+	5.48418i	0.182981	+	0.284725i
$372$		0			0
$373$	−15.1132	+	6.90198i	−0.782533	+	0.357371i	−0.766288	−	0.642497i	$-0.777899\pi$
$373$	−15.1132	+	6.90198i	−0.782533	+	0.357371i	−0.0162452	+	0.999868i	$0.505171\pi$
$374$		0			0
$375$	−2.03348	−	12.3468i	−0.105009	−	0.637584i
$376$		0			0
$377$	4.42086	+	2.01894i	0.227686	+	0.103981i
$378$		0			0
$379$	−3.73095	+	3.23289i	−0.191646	+	0.166062i	−0.745399	−	0.666619i	$-0.767741\pi$
$379$	−3.73095	+	3.23289i	−0.191646	+	0.166062i	0.553753	+	0.832681i	$0.313195\pi$
$380$		0			0
$381$	−5.18533	+	11.9971i	−0.265652	+	0.614630i
$382$		0			0
$383$	23.7444	+	15.2596i	1.21328	+	0.779728i	0.981205	−	0.192970i	$-0.0618121\pi$
$383$	23.7444	+	15.2596i	1.21328	+	0.779728i	0.232075	+	0.972698i	$0.425448\pi$
$384$		0			0
$385$	36.7920	+	5.28989i	1.87509	+	0.269598i
$386$		0			0
$387$	33.5260	+	3.42933i	1.70422	+	0.174322i
$388$		0			0
$389$	6.05193	−	6.98429i	0.306845	−	0.354118i	−0.581294	−	0.813694i	$-0.697453\pi$
$389$	6.05193	−	6.98429i	0.306845	−	0.354118i	0.888138	+	0.459576i	$0.151999\pi$
$390$		0			0
$391$	16.8005	+	21.8112i	0.849640	+	1.10304i
$392$		0			0
$393$	−7.40536	+	6.68651i	−0.373551	+	0.337290i
$394$		0			0
$395$	8.77588	−	1.26178i	0.441562	−	0.0634871i
$396$		0			0
$397$	−2.09204	+	14.5504i	−0.104996	+	0.730265i	0.867515	+	0.497411i	$0.165716\pi$
$397$	−2.09204	+	14.5504i	−0.104996	+	0.730265i	−0.972512	+	0.232855i	$0.925193\pi$
$398$		0			0
$399$	25.6754	−	30.8841i	1.28538	−	1.54614i
$400$		0			0
$401$	16.1408	+	4.73937i	0.806034	+	0.236673i	0.658692	−	0.752413i	$-0.271110\pi$
$401$	16.1408	+	4.73937i	0.806034	+	0.236673i	0.147342	+	0.989086i	$0.452928\pi$
$402$		0			0
$403$	−8.37708	−	9.66766i	−0.417292	−	0.481581i
$404$		0			0
$405$	19.3571	−	14.8051i	0.961863	−	0.735669i
$406$		0			0
$407$	−0.463629	−	1.57898i	−0.0229813	−	0.0782670i
$408$		0			0
$409$	−2.95935	−	6.48008i	−0.146331	−	0.320419i	0.822247	−	0.569131i	$-0.192720\pi$
$409$	−2.95935	−	6.48008i	−0.146331	−	0.320419i	−0.968578	+	0.248711i	$0.919993\pi$
$410$		0			0
$411$	5.59556	+	11.6183i	0.276009	+	0.573090i
$412$		0			0
$413$	−61.7559			−3.03881
$414$		0			0
$415$	33.2190			1.63066
$416$		0			0
$417$	−1.12047	−	2.32648i	−0.0548696	−	0.113928i
$418$		0			0
$419$	13.1690	+	28.8361i	0.643348	+	1.40874i	0.897257	+	0.441508i	$0.145556\pi$
$419$	13.1690	+	28.8361i	0.643348	+	1.40874i	−0.253909	+	0.967228i	$0.581716\pi$
$420$		0			0
$421$	−5.97793	−	20.3590i	−0.291347	−	0.992236i	−0.966949	−	0.254970i	$-0.917935\pi$
$421$	−5.97793	−	20.3590i	−0.291347	−	0.992236i	0.675602	−	0.737266i	$-0.263884\pi$
$422$		0			0
$423$	2.97868	+	2.37510i	0.144828	+	0.115481i
$424$		0			0
$425$	−8.76667	−	10.1173i	−0.425246	−	0.490760i
$426$		0			0
$427$	24.5152	+	7.19833i	1.18638	+	0.348351i
$428$		0			0
$429$	−5.40716	+	6.50408i	−0.261060	+	0.314020i
$430$		0			0
$431$	−2.37596	+	16.5252i	−0.114446	+	0.795989i	0.849059	+	0.528298i	$0.177170\pi$
$431$	−2.37596	+	16.5252i	−0.114446	+	0.795989i	−0.963505	+	0.267691i	$0.913739\pi$
$432$		0			0
$433$	−1.85441	+	0.266623i	−0.0891171	+	0.0128131i	−0.186729	−	0.982411i	$-0.559789\pi$
$433$	−1.85441	+	0.266623i	−0.0891171	+	0.0128131i	0.0976120	+	0.995225i	$0.468880\pi$
$434$		0			0
$435$	10.5683	−	9.54242i	0.506711	−	0.457524i
$436$		0			0
$437$	14.5364	−	19.9854i	0.695372	−	0.956030i
$438$		0			0
$439$	−5.91959	+	6.83157i	−0.282527	+	0.326053i	−0.879220	−	0.476416i	$-0.841936\pi$
$439$	−5.91959	+	6.83157i	−0.282527	+	0.326053i	0.596693	+	0.802469i	$0.296481\pi$
$440$		0			0
$441$	4.04467	−	39.5417i	0.192603	−	1.88294i
$442$		0			0
$443$	−31.9802	−	4.59806i	−1.51943	−	0.218461i	−0.668487	−	0.743724i	$-0.733058\pi$
$443$	−31.9802	−	4.59806i	−1.51943	−	0.218461i	−0.850940	+	0.525264i	$0.823967\pi$
$444$		0			0
$445$	3.57444	+	2.29715i	0.169445	+	0.108895i
$446$		0			0
$447$	1.75170	−	4.05284i	0.0828526	−	0.191693i
$448$		0			0
$449$	−23.7654	+	20.5928i	−1.12156	+	0.971835i	−0.999785	−	0.0207235i	$-0.993403\pi$
$449$	−23.7654	+	20.5928i	−1.12156	+	0.971835i	−0.121772	+	0.992558i	$0.538858\pi$
$450$		0			0
$451$	9.68760	+	4.42418i	0.456171	+	0.208326i
$452$		0			0
$453$	3.07342	+	18.6610i	0.144402	+	0.876769i
$454$		0			0
$455$	−17.7425	+	8.10274i	−0.831782	+	0.379862i
$456$		0			0
$457$	7.46455	+	11.6151i	0.349177	+	0.543330i	0.970770	−	0.240010i	$-0.0771508\pi$
$457$	7.46455	+	11.6151i	0.349177	+	0.543330i	−0.621594	+	0.783340i	$0.713514\pi$
$458$		0			0
$459$	−10.7062	+	27.8422i	−0.499723	+	1.29956i
$460$		0			0
$461$		−	16.4095i		−	0.764268i	−0.924107	−	0.382134i	$-0.875189\pi$
$461$		−	16.4095i		−	0.764268i	0.924107	−	0.382134i	$-0.124811\pi$
$462$		0			0
$463$	13.9081	−	8.93817i	0.646362	−	0.415392i	−0.175973	−	0.984395i	$-0.556307\pi$
$463$	13.9081	−	8.93817i	0.646362	−	0.415392i	0.822335	+	0.569003i	$0.192671\pi$
$464$		0			0
$465$	−35.7369	+	11.2914i	−1.65726	+	0.523624i
$466$		0			0
$467$	−0.225434	+	0.0661933i	−0.0104318	+	0.00306306i	−0.286944	−	0.957947i	$-0.592639\pi$
$467$	−0.225434	+	0.0661933i	−0.0104318	+	0.00306306i	0.276512	+	0.961010i	$0.410821\pi$
$468$		0			0
$469$	−22.8886	+	50.1191i	−1.05690	+	2.31428i
$470$		0			0
$471$	−19.8935	−	29.6069i	−0.916645	−	1.36421i
$472$		0			0
$473$	−9.65468	+	32.8808i	−0.443923	+	1.51186i
$474$		0			0
$475$	−6.49659	+	10.1089i	−0.298084	+	0.463828i
$476$		0			0
$477$	−1.64242	+	4.02382i	−0.0752013	+	0.184238i
$478$		0			0
$479$	−4.01185	−	27.9030i	−0.183306	−	1.27492i	−0.848878	−	0.528589i	$-0.822721\pi$
$479$	−4.01185	−	27.9030i	−0.183306	−	1.27492i	0.665572	−	0.746334i	$-0.268188\pi$
$480$		0			0
$481$	0.652627	+	0.565505i	0.0297572	+	0.0257848i
$482$		0			0
$483$	1.39084	−	37.3533i	0.0632853	−	1.69964i
$484$		0			0
$485$	16.0754	+	13.9294i	0.729947	+	0.632503i
$486$		0			0
$487$	2.85231	+	19.8383i	0.129251	+	0.898958i	0.946507	+	0.322684i	$0.104585\pi$
$487$	2.85231	+	19.8383i	0.129251	+	0.898958i	−0.817256	+	0.576275i	$0.804506\pi$
$488$		0			0
$489$	20.3987	+	5.53949i	0.922459	+	0.250504i
$490$		0			0
$491$	−17.5090	+	27.2445i	−0.790170	+	1.22953i	0.179173	+	0.983817i	$0.442658\pi$
$491$	−17.5090	+	27.2445i	−0.790170	+	1.22953i	−0.969343	+	0.245711i	$0.920979\pi$
$492$		0			0
$493$	−4.91033	+	16.7230i	−0.221150	+	0.753168i
$494$		0			0
$495$	11.2065	+	22.1018i	0.503697	+	0.993404i
$496$		0			0
$497$	−11.2959	+	24.7347i	−0.506692	+	1.10950i
$498$		0			0
$499$	−16.8909	+	4.95960i	−0.756139	+	0.222022i	−0.637009	−	0.770856i	$-0.719829\pi$
$499$	−16.8909	+	4.95960i	−0.756139	+	0.222022i	−0.119130	+	0.992879i	$0.538010\pi$
$500$		0			0
$501$	−7.65965	−	24.2426i	−0.342208	−	1.08308i
$502$		0			0
$503$	−1.82660	+	1.17389i	−0.0814442	+	0.0523410i	−0.580729	−	0.814097i	$-0.697232\pi$
$503$	−1.82660	+	1.17389i	−0.0814442	+	0.0523410i	0.499285	+	0.866438i	$0.333596\pi$
$504$		0			0
$505$		−	14.3755i		−	0.639700i
$506$		0			0
$507$	−2.20666	+	17.9431i	−0.0980012	+	0.796879i
$508$		0			0
$509$	−16.0865	−	25.0311i	−0.713022	−	1.10948i	−0.988942	−	0.148303i	$-0.952619\pi$
$509$	−16.0865	−	25.0311i	−0.713022	−	1.10948i	0.275920	−	0.961181i	$-0.411018\pi$
$510$		0			0
$511$	18.4208	−	8.41248i	0.814887	−	0.372146i
$512$		0			0
$513$	26.6868	+	2.17984i	1.17825	+	0.0962422i
$514$		0			0
$515$	7.04163	+	3.21580i	0.310291	+	0.141705i
$516$		0			0
$517$	−2.92769	+	2.53686i	−0.128760	+	0.111571i
$518$		0			0
$519$	−35.9566	−	15.5410i	−1.57832	−	0.682173i
$520$		0			0
$521$	−1.64422	−	1.05668i	−0.0720346	−	0.0462938i	0.504128	−	0.863629i	$-0.331814\pi$
$521$	−1.64422	−	1.05668i	−0.0720346	−	0.0462938i	−0.576162	+	0.817335i	$0.695450\pi$
$522$		0			0
$523$	28.4417	+	4.08931i	1.24367	+	0.178813i	0.732560	−	0.680702i	$-0.238325\pi$
$523$	28.4417	+	4.08931i	1.24367	+	0.178813i	0.511111	+	0.859515i	$0.329234\pi$
$524$		0			0
$525$	0.371348	+	18.1716i	0.0162070	+	0.793075i
$526$		0			0
$527$	30.0418	−	34.6701i	1.30864	−	1.51025i
$528$		0			0
$529$	−0.632402	−	22.9913i	−0.0274958	−	0.999622i
$530$		0			0
$531$	−23.6553	−	33.6972i	−1.02655	−	1.46233i
$532$		0			0
$533$	−5.53172	+	0.795342i	−0.239606	+	0.0344501i
$534$		0			0
$535$	6.69707	−	46.5792i	0.289540	−	2.01379i
$536$		0			0
$537$	−16.3994	−	13.6336i	−0.707685	−	0.588333i
$538$		0			0
$539$	38.7809	+	11.3871i	1.67041	+	0.490477i
$540$		0			0
$541$	−21.1280	−	24.3830i	−0.908364	−	1.04831i	−0.998627	−	0.0523898i	$-0.983316\pi$
$541$	−21.1280	−	24.3830i	−0.908364	−	1.04831i	0.0902629	−	0.995918i	$-0.471229\pi$
$542$		0			0
$543$	6.42979	−	10.4693i	0.275929	−	0.449279i
$544$		0			0
$545$	0.116505	+	0.396779i	0.00499052	+	0.0169961i
$546$		0			0
$547$	−12.0533	−	26.3931i	−0.515363	−	1.12849i	−0.971165	−	0.238407i	$-0.923375\pi$
$547$	−12.0533	−	26.3931i	−0.515363	−	1.12849i	0.455802	−	0.890081i	$-0.349352\pi$
$548$		0			0
$549$	5.46266	+	16.1341i	0.233141	+	0.688585i
$550$		0			0
$551$	15.6446			0.666483
$552$		0			0
$553$	14.7343			0.626566
$554$		0			0
$555$	2.27943	−	1.09781i	0.0967564	−	0.0465993i
$556$		0			0
$557$	5.03220	+	11.0190i	0.213221	+	0.466889i	0.985777	−	0.168058i	$-0.0537494\pi$
$557$	5.03220	+	11.0190i	0.213221	+	0.466889i	−0.772556	+	0.634946i	$0.781022\pi$
$558$		0			0
$559$	−5.06631	−	17.2543i	−0.214282	−	0.729777i
$560$		0			0
$561$	−25.8471	−	15.8742i	−1.09126	−	0.670211i
$562$		0			0
$563$	−4.77199	−	5.50716i	−0.201115	−	0.232099i	0.646229	−	0.763144i	$-0.276345\pi$
$563$	−4.77199	−	5.50716i	−0.201115	−	0.232099i	−0.847344	+	0.531044i	$0.821800\pi$
$564$		0			0
$565$	29.8025	+	8.75081i	1.25380	+	0.368149i
$566$		0			0
$567$	35.3430	−	19.7755i	1.48427	−	0.830491i
$568$		0			0
$569$	4.13701	−	28.7735i	0.173432	−	1.20625i	−0.698132	−	0.715969i	$-0.745985\pi$
$569$	4.13701	−	28.7735i	0.173432	−	1.20625i	0.871565	−	0.490280i	$-0.163106\pi$
$570$		0			0
$571$	−22.1502	+	3.18472i	−0.926959	+	0.133277i	−0.589229	−	0.807966i	$-0.700568\pi$
$571$	−22.1502	+	3.18472i	−0.926959	+	0.133277i	−0.337730	+	0.941243i	$0.609659\pi$
$572$		0			0
$573$	26.7852	+	29.6648i	1.11897	+	1.23926i
$574$		0			0
$575$	0.951129	+	11.1431i	0.0396648	+	0.464700i
$576$		0			0
$577$	−6.65149	+	7.67623i	−0.276905	+	0.319566i	−0.877118	−	0.480275i	$-0.840537\pi$
$577$	−6.65149	+	7.67623i	−0.276905	+	0.319566i	0.600213	+	0.799840i	$0.295082\pi$
$578$		0			0
$579$	−8.40607	+	0.171783i	−0.349344	+	0.00713907i
$580$		0			0
$581$	54.6437	+	7.85657i	2.26700	+	0.325946i
$582$		0			0
$583$	−3.71781	−	2.38929i	−0.153976	−	0.0989543i
$584$		0			0
$585$	−11.2174	−	6.57751i	−0.463784	−	0.271947i
$586$		0			0
$587$	9.96085	−	8.63113i	0.411128	−	0.356245i	−0.424606	−	0.905378i	$-0.639588\pi$
$587$	9.96085	−	8.63113i	0.411128	−	0.356245i	0.835735	+	0.549133i	$0.185042\pi$
$588$		0			0
$589$	−37.4570	−	17.1061i	−1.54339	−	0.704843i
$590$		0			0
$591$	−12.2474	+	2.01712i	−0.503791	+	0.0829732i
$592$		0			0
$593$	−22.0939	+	10.0899i	−0.907286	+	0.414344i	−0.813712	−	0.581268i	$-0.802557\pi$
$593$	−22.0939	+	10.0899i	−0.907286	+	0.414344i	−0.0935745	+	0.995612i	$0.529829\pi$
$594$		0			0
$595$	−37.8174	−	58.8450i	−1.55036	−	2.41241i
$596$		0			0
$597$	33.7781	+	4.15407i	1.38245	+	0.170015i
$598$		0			0
$599$			12.4098i			0.507051i	0.967329	+	0.253526i	$0.0815902\pi$
$599$			12.4098i			0.507051i	−0.967329	+	0.253526i	$0.918410\pi$
$600$		0			0
$601$	−33.7383	+	21.6823i	−1.37621	+	0.884440i	−0.999129	−	0.0417386i	$-0.986710\pi$
$601$	−33.7383	+	21.6823i	−1.37621	+	0.884440i	−0.377086	+	0.926178i	$0.623074\pi$
$602$		0			0
$603$	−36.1149	+	6.70866i	−1.47071	+	0.273198i
$604$		0			0
$605$	4.40120	−	1.29231i	0.178934	−	0.0525399i
$606$		0			0
$607$	−16.2704	+	35.6272i	−0.660396	+	1.44606i	0.221758	+	0.975102i	$0.428821\pi$
$607$	−16.2704	+	35.6272i	−0.660396	+	1.44606i	−0.882153	+	0.470963i	$0.843907\pi$
$608$		0			0
$609$	19.6412	−	13.1973i	0.795900	−	0.534782i
$610$		0			0
$611$	0.572714	−	1.95049i	0.0231695	−	0.0789082i
$612$		0			0
$613$	−11.6512	+	18.1297i	−0.470588	+	0.732250i	−0.992698	−	0.120629i	$-0.961509\pi$
$613$	−11.6512	+	18.1297i	−0.470588	+	0.732250i	0.522109	+	0.852879i	$0.325145\pi$
$614$		0			0
$615$	−4.29099	+	15.8012i	−0.173029	+	0.637164i
$616$		0			0
$617$	2.24062	+	15.5838i	0.0902038	+	0.627382i	0.983901	+	0.178712i	$0.0571930\pi$
$617$	2.24062	+	15.5838i	0.0902038	+	0.627382i	−0.893698	+	0.448670i	$0.851898\pi$
$618$		0			0
$619$	−8.41259	−	7.28955i	−0.338131	−	0.292992i	0.469199	−	0.883092i	$-0.344543\pi$
$619$	−8.41259	−	7.28955i	−0.338131	−	0.292992i	−0.807330	+	0.590101i	$0.799088\pi$
$620$		0			0
$621$	20.9146	−	13.5491i	0.839276	−	0.543706i
$622$		0			0
$623$	5.33648	+	4.62408i	0.213801	+	0.185260i
$624$		0			0
$625$	4.44332	+	30.9040i	0.177733	+	1.23616i
$626$		0			0
$627$	−7.13538	+	26.2754i	−0.284960	+	1.04934i
$628$		0			0
$629$	−1.67428	+	2.60524i	−0.0667581	+	0.103878i
$630$		0			0
$631$	1.89337	−	6.44824i	0.0753740	−	0.256700i	−0.913183	−	0.407551i	$-0.866383\pi$
$631$	1.89337	−	6.44824i	0.0753740	−	0.256700i	0.988557	+	0.150850i	$0.0482012\pi$
$632$		0			0
$633$	15.2309	−	10.2340i	0.605376	−	0.406765i
$634$		0			0
$635$	8.48785	−	18.5858i	0.336830	−	0.737555i
$636$		0			0
$637$	−20.3503	+	5.97539i	−0.806308	+	0.236753i
$638$		0			0
$639$	−17.8234	+	3.31084i	−0.705081	+	0.130975i
$640$		0			0
$641$	6.70062	−	4.30623i	0.264659	−	0.170086i	−0.401581	−	0.915824i	$-0.631539\pi$
$641$	6.70062	−	4.30623i	0.264659	−	0.170086i	0.666240	+	0.745738i	$0.267903\pi$
$642$		0			0
$643$		−	49.5727i		−	1.95496i	−0.211038	−	0.977478i	$-0.567684\pi$
$643$		−	49.5727i		−	1.95496i	0.211038	−	0.977478i	$-0.432316\pi$
$644$		0			0
$645$	−52.2915	−	6.43087i	−2.05897	−	0.253215i
$646$		0			0
$647$	−25.4936	−	39.6688i	−1.00226	−	1.55954i	−0.816824	−	0.576886i	$-0.804267\pi$
$647$	−25.4936	−	39.6688i	−1.00226	−	1.55954i	−0.185433	−	0.982657i	$-0.559369\pi$
$648$		0			0
$649$	38.0820	−	17.3915i	1.49485	−	0.682675i
$650$		0			0
$651$	−61.4559	+	10.1217i	−2.40865	+	0.396699i
$652$		0			0
$653$	10.4472	+	4.77106i	0.408829	+	0.186706i	0.609205	−	0.793013i	$-0.291489\pi$
$653$	10.4472	+	4.77106i	0.408829	+	0.186706i	−0.200375	+	0.979719i	$0.564216\pi$
$654$		0			0
$655$	11.7881	−	10.2145i	0.460600	−	0.399113i
$656$		0			0
$657$	11.6463	+	6.82895i	0.454364	+	0.266423i
$658$		0			0
$659$	−21.4550	−	13.7883i	−0.835766	−	0.537114i	0.0513391	−	0.998681i	$-0.483651\pi$
$659$	−21.4550	−	13.7883i	−0.835766	−	0.537114i	−0.887105	+	0.461567i	$0.847287\pi$
$660$		0			0
$661$	−29.5593	−	4.24998i	−1.14972	−	0.165305i	−0.459008	−	0.888432i	$-0.651795\pi$
$661$	−29.5593	−	4.24998i	−1.14972	−	0.165305i	−0.690715	+	0.723127i	$0.742704\pi$
$662$		0			0
$663$	15.9137	−	0.325206i	0.618037	−	0.0126300i
$664$		0			0
$665$	−41.1171	+	47.4517i	−1.59445	+	1.84010i
$666$		0			0
$667$	11.5350	−	8.88510i	0.446639	−	0.344032i
$668$		0			0
$669$	8.97665	+	9.94170i	0.347057	+	0.384368i
$670$		0			0
$671$	−17.1446	+	2.46502i	−0.661859	+	0.0951609i
$672$		0			0
$673$	−5.47910	+	38.1080i	−0.211204	+	1.46895i	0.557942	+	0.829880i	$0.311591\pi$
$673$	−5.47910	+	38.1080i	−0.211204	+	1.46895i	−0.769146	+	0.639074i	$0.779318\pi$
$674$		0			0
$675$	−9.77313	+	7.16318i	−0.376168	+	0.275711i
$676$		0			0
$677$	−39.6972	−	11.6562i	−1.52569	−	0.447982i	−0.591960	−	0.805967i	$-0.701646\pi$
$677$	−39.6972	−	11.6562i	−1.52569	−	0.447982i	−0.933727	+	0.357985i	$0.883464\pi$
$678$		0			0
$679$	23.1488	+	26.7152i	0.888371	+	1.02523i
$680$		0			0
$681$	22.0918	+	13.5679i	0.846560	+	0.519923i
$682$		0			0
$683$	−1.58915	−	5.41216i	−0.0608073	−	0.207091i	0.923486	−	0.383633i	$-0.125327\pi$
$683$	−1.58915	−	5.41216i	−0.0608073	−	0.207091i	−0.984293	+	0.176542i	$0.943509\pi$
$684$		0			0
$685$	−8.37475	−	18.3382i	−0.319983	−	0.700665i
$686$		0			0
$687$	−25.0632	+	12.0708i	−0.956221	+	0.460530i
$688$		0			0
$689$	2.31907			0.0883495
$690$		0			0
$691$	35.8032			1.36202			0.681008	−	0.732276i	$-0.261542\pi$
$691$	35.8032			1.36202			0.681008	+	0.732276i	$0.261542\pi$
$692$		0			0
$693$	13.2069	+	39.0069i	0.501690	+	1.48175i
$694$		0			0
$695$	1.67698	+	3.67208i	0.0636115	+	0.139290i
$696$		0			0
$697$	−5.64643	−	19.2300i	−0.213874	−	0.728387i
$698$		0			0
$699$	20.3583	−	33.1482i	0.770022	−	1.25378i
$700$		0			0
$701$	−10.9892	−	12.6822i	−0.415057	−	0.479001i	0.509268	−	0.860608i	$-0.329916\pi$
$701$	−10.9892	−	12.6822i	−0.415057	−	0.479001i	−0.924325	+	0.381607i	$0.875371\pi$
$702$		0			0
$703$	2.66718	+	0.783156i	0.100595	+	0.0295373i
$704$		0			0
$705$	−4.57981	−	3.80742i	−0.172486	−	0.143396i
$706$		0			0
$707$	3.39991	−	23.6469i	0.127867	−	0.889334i
$708$		0			0
$709$	14.7219	−	2.11669i	0.552892	−	0.0794939i	0.139794	−	0.990181i	$-0.455356\pi$
$709$	14.7219	−	2.11669i	0.552892	−	0.0794939i	0.413098	+	0.910687i	$0.364447\pi$
$710$		0			0
$711$	5.64390	+	8.03979i	0.211663	+	0.301516i
$712$		0			0
$713$	−37.3328	+	8.66051i	−1.39813	+	0.324339i
$714$		0			0
$715$	8.65912	−	9.99316i	0.323833	−	0.373723i
$716$		0			0
$717$	−0.179013	−	8.75987i	−0.00668538	−	0.327143i
$718$		0			0
$719$	−14.8613	−	2.13673i	−0.554233	−	0.0796867i	−0.140493	−	0.990082i	$-0.544869\pi$
$719$	−14.8613	−	2.13673i	−0.554233	−	0.0796867i	−0.413740	+	0.910395i	$0.635778\pi$
$720$		0			0
$721$	10.8226	+	6.95524i	0.403053	+	0.259027i
$722$		0			0
$723$	37.9281	+	16.3931i	1.41056	+	0.609667i
$724$		0			0
$725$	−5.35060	+	4.63632i	−0.198716	+	0.172189i
$726$		0			0
$727$	22.2806	+	10.1752i	0.826341	+	0.377377i	0.783260	−	0.621694i	$-0.213555\pi$
$727$	22.2806	+	10.1752i	0.826341	+	0.377377i	0.0430808	+	0.999072i	$0.486283\pi$
$728$		0			0
$729$	24.3285	+	11.7101i	0.901054	+	0.433706i
$730$		0			0
$731$	58.6615	−	26.7898i	2.16967	−	0.990857i
$732$		0			0
$733$	−0.748566	−	1.16479i	−0.0276489	−	0.0430225i	0.827154	−	0.561975i	$-0.189958\pi$
$733$	−0.748566	−	1.16479i	−0.0276489	−	0.0430225i	−0.854803	+	0.518953i	$0.826322\pi$
$734$		0			0
$735$	−7.58481	+	61.6745i	−0.279770	+	2.27490i
$736$		0			0
$737$		−	37.3519i		−	1.37588i
$738$		0			0
$739$	−44.2652	+	28.4475i	−1.62832	+	1.04646i	−0.678057	+	0.735009i	$0.737178\pi$
$739$	−44.2652	+	28.4475i	−1.62832	+	1.04646i	−0.950263	+	0.311449i	$0.899186\pi$
$740$		0			0
$741$	−4.30447	−	13.6236i	−0.158129	−	0.500474i
$742$		0			0
$743$	38.9231	−	11.4288i	1.42795	−	0.419284i	0.525763	−	0.850631i	$-0.323780\pi$
$743$	38.9231	−	11.4288i	1.42795	−	0.419284i	0.902186	+	0.431348i	$0.141962\pi$
$744$		0			0
$745$	−2.86735	+	6.27863i	−0.105052	+	0.230031i
$746$		0			0
$747$	16.6440	+	32.8258i	0.608973	+	1.20103i
$748$		0			0
$749$	22.0327	−	75.0365i	0.805058	−	2.74177i
$750$		0			0
$751$	0.268975	−	0.418534i	0.00981505	−	0.0152725i	−0.836311	−	0.548255i	$-0.815292\pi$
$751$	0.268975	−	0.418534i	0.00981505	−	0.0152725i	0.846126	+	0.532982i	$0.178929\pi$
$752$		0			0
$753$	−36.6249	−	9.94592i	−1.33469	−	0.362449i
$754$		0			0
$755$	−4.20770	−	29.2652i	−0.153134	−	1.06507i
$756$		0			0
$757$	11.1942	+	9.69981i	0.406859	+	0.352546i	0.834120	−	0.551583i	$-0.185976\pi$
$757$	11.1942	+	9.69981i	0.406859	+	0.352546i	−0.427261	+	0.904128i	$0.640521\pi$
$758$		0			0
$759$	9.66163	+	23.4257i	0.350695	+	0.850300i
$760$		0			0
$761$	12.9871	+	11.2534i	0.470784	+	0.407936i	0.857678	−	0.514188i	$-0.171907\pi$
$761$	12.9871	+	11.2534i	0.470784	+	0.407936i	−0.386894	+	0.922124i	$0.626452\pi$
$762$		0			0
$763$	0.0978032	+	0.680236i	0.00354071	+	0.0246262i
$764$		0			0
$765$	17.6231	−	43.1754i	0.637164	−	1.56101i
$766$		0			0
$767$	−11.8773	+	18.4814i	−0.428863	+	0.667324i
$768$		0			0
$769$	−7.99079	+	27.2141i	−0.288155	+	0.981366i	0.680457	+	0.732788i	$0.261781\pi$
$769$	−7.99079	+	27.2141i	−0.288155	+	0.981366i	−0.968612	+	0.248578i	$0.920037\pi$
$770$		0			0
$771$	13.2159	+	19.6688i	0.475959	+	0.708356i
$772$		0			0
$773$	−0.334016	+	0.731392i	−0.0120137	+	0.0263063i	−0.915544	−	0.402218i	$-0.868239\pi$
$773$	−0.334016	+	0.731392i	−0.0120137	+	0.0263063i	0.903530	+	0.428525i	$0.140967\pi$
$774$		0			0
$775$	17.8801	−	5.25007i	0.642272	−	0.188588i
$776$		0			0
$777$	4.00919	−	1.26674i	0.143829	−	0.0454439i
$778$		0			0
$779$	−15.1340	+	9.72605i	−0.542233	+	0.348472i
$780$		0			0
$781$		−	18.4338i		−	0.659615i
$782$		0			0
$783$	14.7246	+	5.66206i	0.526214	+	0.202346i
$784$		0			0
$785$	30.1478	+	46.9110i	1.07602	+	1.67432i
$786$		0			0
$787$	−3.39219	+	1.54916i	−0.120918	+	0.0552216i	−0.474956	−	0.880010i	$-0.657536\pi$
$787$	−3.39219	+	1.54916i	−0.120918	+	0.0552216i	0.354037	+	0.935231i	$0.384809\pi$
$788$		0			0
$789$	6.41061	+	38.9235i	0.228224	+	1.38571i
$790$		0			0
$791$	46.9540	+	21.4432i	1.66949	+	0.762432i
$792$		0			0
$793$	6.86912	−	5.95213i	0.243930	−	0.211366i
$794$		0			0
$795$	2.69562	−	6.23676i	0.0956039	−	0.221195i
$796$		0			0
$797$	−22.0226	−	14.1530i	−0.780079	−	0.501326i	0.0889808	−	0.996033i	$-0.471639\pi$
$797$	−22.0226	−	14.1530i	−0.780079	−	0.501326i	−0.869060	+	0.494707i	$0.835275\pi$
$798$		0			0
$799$	7.21591	+	1.03749i	0.255280	+	0.0367038i
$800$		0			0
$801$	−0.479027	+	4.68309i	−0.0169256	+	0.165469i
$802$		0			0
$803$	−8.99014	+	10.3752i	−0.317255	+	0.366132i
$804$		0			0
$805$	−3.36697	+	58.3387i	−0.118670	+	2.05617i
$806$		0			0
$807$	−5.71359	+	5.15896i	−0.201128	+	0.181604i
$808$		0			0
$809$	34.8697	−	5.01351i	1.22595	−	0.176266i	0.501235	−	0.865311i	$-0.332879\pi$
$809$	34.8697	−	5.01351i	1.22595	−	0.176266i	0.724718	+	0.689045i	$0.241970\pi$
$810$		0			0
$811$	−1.76468	+	12.2737i	−0.0619665	+	0.430986i	0.935096	+	0.354394i	$0.115313\pi$
$811$	−1.76468	+	12.2737i	−0.0619665	+	0.430986i	−0.997063	+	0.0765919i	$0.975596\pi$
$812$		0			0
$813$	6.14866	−	7.39601i	0.215643	−	0.259389i
$814$		0			0
$815$	−31.7061	−	9.30976i	−1.11062	−	0.326107i
$816$		0			0
$817$	−37.9077	−	43.7478i	−1.32622	−	1.53054i
$818$		0			0
$819$	−16.8965	−	13.4727i	−0.590412	−	0.470774i
$820$		0			0
$821$	−1.32330	−	4.50675i	−0.0461836	−	0.157287i	0.933173	−	0.359428i	$-0.117028\pi$
$821$	−1.32330	−	4.50675i	−0.0461836	−	0.157287i	−0.979356	+	0.202141i	$0.935210\pi$
$822$		0			0
$823$	20.0801	+	43.9693i	0.699949	+	1.53267i	0.840034	+	0.542534i	$0.182535\pi$
$823$	20.0801	+	43.9693i	0.699949	+	1.53267i	−0.140085	+	0.990139i	$0.544738\pi$
$824$		0			0
$825$	−5.34642	−	11.1010i	−0.186138	−	0.386488i
$826$		0			0
$827$	29.8929			1.03948			0.519738	−	0.854326i	$-0.326030\pi$
$827$	29.8929			1.03948			0.519738	+	0.854326i	$0.326030\pi$
$828$		0			0
$829$	46.0631			1.59984			0.799919	−	0.600108i	$-0.204876\pi$
$829$	46.0631			1.59984			0.799919	+	0.600108i	$0.204876\pi$
$830$		0			0
$831$	−5.68239	−	11.7986i	−0.197120	−	0.409289i
$832$		0			0
$833$	−31.5969	−	69.1875i	−1.09477	−	2.39721i
$834$		0			0
$835$	11.1977	+	38.1358i	0.387512	+	1.31975i
$836$		0			0
$837$	−29.0633	−	29.6565i	−1.00457	−	1.02508i
$838$		0			0
$839$	34.4396	+	39.7454i	1.18899	+	1.37217i	0.911429	+	0.411456i	$0.134980\pi$
$839$	34.4396	+	39.7454i	1.18899	+	1.37217i	0.277558	+	0.960709i	$0.410475\pi$
$840$		0			0
$841$	−18.9812	−	5.57338i	−0.654523	−	0.192185i
$842$		0			0
$843$	21.0129	−	25.2757i	0.723723	−	0.870542i
$844$		0			0
$845$	4.02212	−	27.9745i	0.138365	−	0.962351i
$846$		0			0
$847$	7.54540	−	1.08487i	0.259263	−	0.0372764i
$848$		0			0
$849$	−8.09356	+	7.30791i	−0.277770	+	0.250807i
$850$		0			0
$851$	2.41134	−	0.937349i	0.0826598	−	0.0321319i
$852$		0			0
$853$	28.4620	−	32.8469i	0.974521	−	1.12466i	−0.0176587	−	0.999844i	$-0.505621\pi$
$853$	28.4620	−	32.8469i	0.974521	−	1.12466i	0.992180	−	0.124814i	$-0.0398333\pi$
$854$		0			0
$855$	−41.6417	−	4.25948i	−1.42412	−	0.145671i
$856$		0			0
$857$	−13.6066	−	1.95633i	−0.464793	−	0.0668271i	−0.0940595	−	0.995567i	$-0.529984\pi$
$857$	−13.6066	−	1.95633i	−0.464793	−	0.0668271i	−0.370733	+	0.928739i	$0.620893\pi$
$858$		0			0
$859$	−6.84032	−	4.39600i	−0.233389	−	0.149990i	0.418720	−	0.908115i	$-0.362479\pi$
$859$	−6.84032	−	4.39600i	−0.233389	−	0.149990i	−0.652108	+	0.758126i	$0.726115\pi$
$860$		0			0
$861$	−10.7956	+	24.9773i	−0.367912	+	0.851223i
$862$		0			0
$863$	41.8531	−	36.2659i	1.42470	−	1.23451i	0.493624	−	0.869676i	$-0.335672\pi$
$863$	41.8531	−	36.2659i	1.42470	−	1.23451i	0.931074	−	0.364832i	$-0.118873\pi$
$864$		0			0
$865$	55.7036	+	25.4390i	1.89398	+	0.864952i
$866$		0			0
$867$	4.49119	+	27.2693i	0.152529	+	0.926112i
$868$		0			0
$869$	−9.08596	+	4.14942i	−0.308220	+	0.140759i
$870$		0			0
$871$	10.5968	+	16.4890i	0.359059	+	0.558707i
$872$		0			0
$873$	−5.71013	+	22.8643i	−0.193259	+	0.773839i
$874$		0			0
$875$			32.5095i			1.09902i
$876$		0			0
$877$	40.3360	−	25.9224i	1.36205	−	0.875336i	0.363631	−	0.931543i	$-0.381537\pi$
$877$	40.3360	−	25.9224i	1.36205	−	0.875336i	0.998419	+	0.0562069i	$0.0179006\pi$
$878$		0			0
$879$	11.8219	−	3.73524i	0.398744	−	0.125986i
$880$		0			0
$881$	−8.65013	+	2.53991i	−0.291430	+	0.0855717i	−0.424180	−	0.905578i	$-0.639438\pi$
$881$	−8.65013	+	2.53991i	−0.291430	+	0.0855717i	0.132750	+	0.991150i	$0.457619\pi$
$882$		0			0
$883$	−3.97573	+	8.70562i	−0.133794	+	0.292968i	−0.964657	−	0.263509i	$-0.915120\pi$
$883$	−3.97573	+	8.70562i	−0.133794	+	0.292968i	0.830863	+	0.556477i	$0.187847\pi$
$884$		0			0
$885$	35.8969	+	53.4242i	1.20666	+	1.79584i
$886$		0			0
$887$	−0.598642	+	2.03879i	−0.0201004	+	0.0684558i	−0.968932	−	0.247325i	$-0.920448\pi$
$887$	−0.598642	+	2.03879i	−0.0201004	+	0.0684558i	0.948832	+	0.315781i	$0.102267\pi$
$888$		0			0
$889$	18.3578	−	28.5653i	0.615701	−	0.958049i
$890$		0			0
$891$	−16.2253	+	22.1478i	−0.543568	+	0.741978i
$892$		0			0
$893$	−0.931269	−	6.47712i	−0.0311637	−	0.216749i
$894$		0			0
$895$	25.1967	+	21.8331i	0.842233	+	0.729799i
$896$		0			0
$897$	−10.9110	−	7.60024i	−0.364309	−	0.253765i
$898$		0			0
$899$	−18.3355	−	15.8878i	−0.611524	−	0.529889i
$900$		0			0
$901$	1.18358	+	8.23196i	0.0394307	+	0.274247i
$902$		0			0
$903$	−84.4959	−	22.9458i	−2.81185	−	0.763589i
$904$		0			0
$905$	−10.3841	+	16.1581i	−0.345181	+	0.537112i
$906$		0			0
$907$	7.71215	−	26.2652i	0.256078	−	0.872121i	−0.726641	−	0.687017i	$-0.758920\pi$
$907$	7.71215	−	26.2652i	0.256078	−	0.872121i	0.982719	−	0.185104i	$-0.0592621\pi$
$908$		0			0
$909$	14.2053	−	7.20267i	0.471160	−	0.238897i
$910$		0			0
$911$	−15.1928	+	33.2676i	−0.503359	+	1.10220i	0.472004	+	0.881597i	$0.343531\pi$
$911$	−15.1928	+	33.2676i	−0.503359	+	1.10220i	−0.975363	+	0.220607i	$0.929196\pi$
$912$		0			0
$913$	−35.9087	+	10.5438i	−1.18841	+	0.348947i
$914$		0			0
$915$	−8.02280	−	25.3920i	−0.265226	−	0.839433i
$916$		0			0
$917$	21.8067	−	14.0143i	0.720121	−	0.462793i
$918$		0			0
$919$		−	13.2258i		−	0.436279i	−0.975918	−	0.218140i	$-0.930001\pi$
$919$		−	13.2258i		−	0.436279i	0.975918	−	0.218140i	$-0.0699988\pi$
$920$		0			0
$921$	4.41046	−	35.8629i	0.145330	−	1.18172i
$922$		0			0
$923$	5.22971	+	8.13759i	0.172138	+	0.267852i
$924$		0			0
$925$	−1.14429	+	0.522581i	−0.0376241	+	0.0171824i
$926$		0			0
$927$	0.350393	+	8.56951i	0.0115084	+	0.281460i
$928$		0			0
$929$	−15.0587	−	6.87708i	−0.494060	−	0.225630i	0.152773	−	0.988261i	$-0.451180\pi$
$929$	−15.0587	−	6.87708i	−0.494060	−	0.225630i	−0.646833	+	0.762632i	$0.723907\pi$
$930$		0			0
$931$	−51.5978	+	44.7097i	−1.69105	+	1.46530i
$932$		0			0
$933$	7.81733	+	3.37877i	0.255928	+	0.110616i
$934$		0			0
$935$	39.8919	+	25.6370i	1.30460	+	0.838419i
$936$		0			0
$937$	−1.01153	−	0.145436i	−0.0330452	−	0.00475118i	0.125772	−	0.992059i	$-0.459859\pi$
$937$	−1.01153	−	0.145436i	−0.0330452	−	0.00475118i	−0.158818	+	0.987308i	$0.550768\pi$
$938$		0			0
$939$	−0.477202	−	23.3515i	−0.0155729	−	0.762047i
$940$		0			0
$941$	−19.4775	+	22.4782i	−0.634947	+	0.732768i	−0.978473	−	0.206375i	$-0.933833\pi$
$941$	−19.4775	+	22.4782i	−0.634947	+	0.732768i	0.343526	+	0.939143i	$0.388379\pi$
$942$		0			0
$943$	−5.63484	+	15.7663i	−0.183496	+	0.513422i
$944$		0			0
$945$	−55.8727	+	29.7801i	−1.81754	+	0.968747i
$946$		0			0
$947$	−0.0512638	+	0.00737063i	−0.00166585	+	0.000239513i	−0.143148	−	0.989701i	$-0.545722\pi$
$947$	−0.0512638	+	0.00737063i	−0.00166585	+	0.000239513i	0.141482	+	0.989941i	$0.454813\pi$
$948$		0			0
$949$	1.02523	−	7.13062i	0.0332803	−	0.231470i
$950$		0			0
$951$	13.1394	+	10.9235i	0.426076	+	0.354217i
$952$		0			0
$953$	−1.67071	−	0.490566i	−0.0541198	−	0.0158910i	0.254561	−	0.967057i	$-0.418069\pi$
$953$	−1.67071	−	0.490566i	−0.0541198	−	0.0158910i	−0.308680	+	0.951166i	$0.599887\pi$
$954$		0			0
$955$	−40.9177	−	47.2215i	−1.32407	−	1.52805i
$956$		0			0
$957$	−8.39521	+	13.6694i	−0.271379	+	0.441870i
$958$		0			0
$959$	−9.43893	−	32.1461i	−0.304799	−	1.03805i
$960$		0			0
$961$	13.6499	+	29.8891i	0.440320	+	0.964166i
$962$		0			0
$963$	49.3833	−	16.7202i	1.59135	−	0.538800i
$964$		0			0
$965$	13.1442			0.423125
$966$		0			0
$967$	−43.3068			−1.39265			−0.696326	−	0.717725i	$-0.745183\pi$
$967$	−43.3068			−1.39265			−0.696326	+	0.717725i	$0.745183\pi$
$968$		0			0
$969$	46.1625	−	22.2325i	1.48295	−	0.714212i
$970$		0			0
$971$	7.91824	+	17.3385i	0.254109	+	0.556420i	0.993097	−	0.117298i	$-0.0374234\pi$
$971$	7.91824	+	17.3385i	0.254109	+	0.556420i	−0.738988	+	0.673718i	$0.764696\pi$
$972$		0			0
$973$	1.89007	+	6.43700i	0.0605930	+	0.206361i
$974$		0			0
$975$	5.50955	+	3.38374i	0.176447	+	0.108367i
$976$		0			0
$977$	0.543273	+	0.626971i	0.0173809	+	0.0200586i	0.764373	−	0.644774i	$-0.223048\pi$
$977$	0.543273	+	0.626971i	0.0173809	+	0.0200586i	−0.746993	+	0.664832i	$0.768503\pi$
$978$		0			0
$979$	−4.59297	−	1.34862i	−0.146792	−	0.0431020i
$980$		0			0
$981$	−0.333709	+	0.313927i	−0.0106545	+	0.0100229i
$982$		0			0
$983$	−0.614504	+	4.27397i	−0.0195996	+	0.136318i	−0.997272	−	0.0738178i	$-0.976482\pi$
$983$	−0.614504	+	4.27397i	−0.0195996	+	0.136318i	0.977672	+	0.210136i	$0.0673908\pi$
$984$		0			0
$985$	19.2071	−	2.76156i	0.611989	−	0.0879907i
$986$		0			0
$987$	−6.63307	−	7.34617i	−0.211133	−	0.233831i
$988$		0			0
$989$	−52.7959	−	10.7270i	−1.67881	−	0.341098i
$990$		0			0
$991$	−24.3189	+	28.0655i	−0.772514	+	0.891529i	−0.996545	−	0.0830531i	$-0.973533\pi$
$991$	−24.3189	+	28.0655i	−0.772514	+	0.891529i	0.224031	+	0.974582i	$0.428078\pi$
$992$		0			0
$993$	6.40418	−	0.130873i	0.203231	−	0.00415314i
$994$		0			0
$995$	−52.6624	−	7.57171i	−1.66951	−	0.240039i
$996$		0			0
$997$	−26.8601	−	17.2619i	−0.850668	−	0.546691i	0.0411151	−	0.999154i	$-0.486909\pi$
$997$	−26.8601	−	17.2619i	−0.850668	−	0.546691i	−0.891783	+	0.452463i	$0.850545\pi$
$998$		0			0
$999$	2.22690	+	1.70240i	0.0704558	+	0.0538616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.53.4	✓	80
3.2	odd	2	inner	276.2.k.a.53.7	yes	80
23.10	odd	22	inner	276.2.k.a.125.7	yes	80
69.56	even	22	inner	276.2.k.a.125.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.53.4	✓	80	1.1	even	1	trivial
276.2.k.a.53.7	yes	80	3.2	odd	2	inner
276.2.k.a.125.4	yes	80	69.56	even	22	inner
276.2.k.a.125.7	yes	80	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.751560 - 1.56050i) q^{3} +(1.12484 + 2.46306i) q^{5} +(1.26778 + 4.31765i) q^{7} +(-1.87032 + 2.34562i) q^{9} +O(q^{10})\)	\(q+(-0.751560 - 1.56050i) q^{3} +(1.12484 + 2.46306i) q^{5} +(1.26778 + 4.31765i) q^{7} +(-1.87032 + 2.34562i) q^{9} +(-1.99770 - 2.30547i) q^{11} +(1.53595 + 0.450995i) q^{13} +(2.99822 - 3.60645i) q^{15} +(-0.816991 + 5.68230i) q^{17} +(5.10053 - 0.733345i) q^{19} +(5.78488 - 5.22334i) q^{21} +(3.34422 - 3.43747i) q^{23} +(-1.52710 + 1.76237i) q^{25} +(5.06599 + 1.15575i) q^{27} +(3.00513 + 0.432072i) q^{29} +(-6.72258 - 4.32034i) q^{31} +(-2.09629 + 4.85010i) q^{33} +(-9.20859 + 7.97929i) q^{35} +(0.490703 + 0.224097i) q^{37} +(-0.450579 - 2.73579i) q^{39} +(-3.17567 + 1.45028i) q^{41} +(-6.07336 - 9.45033i) q^{43} +(-7.88121 - 1.96825i) q^{45} -1.26989i q^{47} +(-11.1461 + 7.16314i) q^{49} +(9.48124 - 2.99567i) q^{51} +(1.39002 - 0.408147i) q^{53} +(3.43141 - 7.51374i) q^{55} +(-4.97774 - 7.40822i) q^{57} +(-3.86643 + 13.1679i) q^{59} +(3.06971 - 4.77657i) q^{61} +(-12.4987 - 5.10165i) q^{63} +(0.616871 + 4.29043i) q^{65} +(9.25358 + 8.01827i) q^{67} +(-7.87755 - 2.63519i) q^{69} +(4.56681 + 3.95716i) q^{71} +(-0.640452 - 4.45444i) q^{73} +(3.89788 + 1.05851i) q^{75} +(7.42156 - 11.5482i) q^{77} +(0.922489 - 3.14171i) q^{79} +(-2.00384 - 8.77409i) q^{81} +(5.09635 - 11.1595i) q^{83} +(-14.9148 + 4.37939i) q^{85} +(-1.58429 - 5.01423i) q^{87} +(1.32007 - 0.848360i) q^{89} +7.20344i q^{91} +(-1.68947 + 13.7376i) q^{93} +(7.54357 + 11.7380i) q^{95} +(7.14563 - 3.26330i) q^{97} +(9.14407 - 0.373885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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